The leaders of India and South Africa have called for a reform of the UN Security Council to address "the gross imbalance of power" in the world body.
Mr Singh said the UN suffered from "a democracy deficit"
Indian Prime Minister Manmohan Singh told the UN World Summit in New York that the council's structure reflected the world of 1945.
South African President Thabo Mbeki criticised "rich and powerful nations" for allegedly blocking the reform.
Both India and South Africa want a permanent seat in the 15-member body.
Earlier on Thursday, Russian President Vladimir Putin urged the gathering of some 150 world leaders carry out "constructive" reform of the UN.
PROPOSED REFORM PACKAGE
No international definition of terrorism
Plans to reform Human Rights Commission deferred to General Assembly
Commitment to break down trade barriers weakened
Creation of peace-building commission to help nations emerging from war agreed
Obligation to intervene when civilians face genocide and war crimes agreed
Development section backing Millennium goals to tackle world poverty
Mr Putin said the reform should "unite, not separate" the world community, stressing that the UN must also play a central role in the fight against terrorism.
Iraqi President Jalal Talabani used his speech to urge leaders to help to overcome the "forces of darkness" in his country.
He said the so-called war on terror required "diverse" international participation.
Israeli Prime Minister Ariel Sharon said this week's withdrawal of the Israeli army from the Gaza Strip offered the Palestinians the opportunity to seize the chance for peace.
On Wednesday, UN Secretary General Kofi Annan said the reform deal was "a good start", but differences had prevented progress.
The summit marking the world body's 60th anniversary began on Wednesday - a day after UN ambassadors reached a watered-down deal on reform.
India has campaigned hard - along with Japan, Brazil and Germany (the Group of Four) - for an expansion of the five permanent seats on the Security Council.
In his speech, Mr Singh said the organisation suffered from a "democracy deficit" as it did not reflect the new realities.
"Until the UN becomes more representative of the contemporary world and more relevant to our concerns and aspirations, its ability to deliver on ... its own charter obligations will remain limited," he said.
He also reaffirmed that India would "never succumb to terrorism" in the disputed territory of Kashmir, which it disputes with Pakistan.
President Pervez Musharraf later denied Pakistan was involved in "cross-border terrorism".
Meanwhile, Mr Mbeki said the council must reform to help reach consensus on global security issues.
"We have not achieved this security consensus because of the gross imbalance of power that defines the relationships among member states," he said.
Mr Mbeki also accused rich nations of using "their power to perpetuate the power imbalance in the ordering of global affairs".
South Africa has played a key role in a bid by the African Union - a rival to the one offered by the Group of Four - to reform the Council.
The current permanent members of the powerful council are China, France, Russia, the UK and the US. Each can veto Security Council resolutions.